The Elders haven't. The Elders are going by the clearly documented government type of every realm readily available, which states the Farronite Republic is a republic. Not a theocracy. Furthermore, nothing in their defines a theocracy. It outlines privileges a theocracy enjoys in Sanguis Astroism, and the responsibilities the Church expects in return. However, nowhere does it say "This defines a theocracy."
I'm an Elder, and I disagree. I'm not the only one. But we can't discuss it in game because you make it a game mechanic issue.